function result_map = ff_abz_vf(varargin)

%% FF_ABZ_VF solve infinite horizon exo shock + endo asset problem

% This program solves the infinite horizon dynamic single asset and single

% shock problem with loops. This file contains codes that processes

% borrowing.

%

% The borrowing problem is very similar to the savings problem. The code

% could be identical if one does not have to deal with default. The main

% addition here in comparison to the savings only code

% <https://fanwangecon.github.io/CodeDynaAsset/m_az/solve/html/ff_az_vf.html

% ff_az_vf> is the ability to deal with default. 

%

% @param param_map container parameter container

%

% @param support_map container support container

%

% @param armt_map container container with states, choices and shocks

% grids that are inputs for grid based solution algorithm

%

% @param func_map container container with function handles for

% consumption cash-on-hand etc.

%

% @return result_map container contains policy function matrix, value

% function matrix, iteration results, and policy function, value function

% and iteration results tables.

%

% keys included in result_map:

%

% * mt_val matrix states_n by shock_n matrix of converged value function grid

% * mt_pol_a matrix states_n by shock_n matrix of converged policy function grid

% * ar_val_diff_norm array if bl_post = true it_iter_last by 1 val function

% difference between iteration

% * ar_pol_diff_norm array if bl_post = true it_iter_last by 1 policy

% function difference between iterations

% * mt_pol_perc_change matrix if bl_post = true it_iter_last by shock_n the

% proportion of grid points at which policy function changed between

% current and last iteration for each element of shock

%

% @example

%

%    % Get Default Parameters

%    it_param_set = 2;

%    [param_map, support_map] = ffs_abz_set_default_param(it_param_set);

%    % Chnage param_map keys for borrowing

%    param_map('fl_b_bd') = -20; % borrow bound

%    param_map('bl_default') = false; % true if allow for default

%    param_map('fl_c_min') = 0.0001; % u(c_min) when default

%    % Change Keys in param_map

%    param_map('it_a_n') = 500;

%    param_map('fl_z_r_borr_n') = 5;

%    param_map('it_z_wage_n') = 15;

%    param_map('it_z_n') = param_map('it_z_wage_n') * param_map('fl_z_r_borr_n');

%    param_map('fl_a_max') = 100;

%    param_map('fl_w') = 1.3;

%    % Change Keys support_map

%    support_map('bl_display') = false;

%    support_map('bl_post') = true;

%    support_map('bl_display_final') = false;

%    % Call Program with external parameters that override defaults.

%    ff_abz_vf(param_map, support_map);

%

% @include

%

% * <https://fanwangecon.github.io/CodeDynaAsset/m_abz/paramfunc/html/ffs_abz_set_default_param.html ffs_abz_set_default_param>

% * <https://fanwangecon.github.io/CodeDynaAsset/m_abz/paramfunc/html/ffs_abz_get_funcgrid.html ffs_abz_get_funcgrid>

% * <https://fanwangecon.github.io/CodeDynaAsset/m_az/solvepost/html/ff_az_vf_post.html ff_az_vf_post>

%

% @seealso

%

% * save loop: <https://fanwangecon.github.io/CodeDynaAsset/m_az/solve/html/ff_az_vf.html ff_az_vf>

% * save vectorized: <https://fanwangecon.github.io/CodeDynaAsset/m_az/solve/html/ff_az_vf_vec.html ff_az_vf_vec>

% * save optimized-vectorized: <https://fanwangecon.github.io/CodeDynaAsset/m_az/solve/html/ff_az_vf_vecsv.html ff_az_vf_vecsv>

% * save + borr loop: <https://fanwangecon.github.io/CodeDynaAsset/m_abz/solve/html/ff_abz_vf.html ff_abz_vf>

% * save + borr vectorized: <https://fanwangecon.github.io/CodeDynaAsset/m_abz/solve/html/ff_abz_vf_vec.html ff_abz_vf_vec>

% * save + borr optimized-vectorized: <https://fanwangecon.github.io/CodeDynaAsset/m_abz/solve/html/ff_abz_vf_vecsv.html ff_abz_vf_vecsv>

%

%% Default

% * it_param_set = 1: quick test

% * it_param_set = 2: benchmark run

% * it_param_set = 3: benchmark profile

% * it_param_set = 4: press publish button

it_param_set = 3;

bl_input_override = true;

[param_map, support_map] = ffs_abz_set_default_param(it_param_set);

% Note: param_map and support_map can be adjusted here or outside to override defaults

param_map('it_a_n') = 75;

param_map('fl_z_r_borr_n') = 3;

param_map('it_z_wage_n') = 5;

param_map('it_z_n') = param_map('it_z_wage_n') * param_map('fl_z_r_borr_n');

% param_map('fl_r_save') = 0.025;

% param_map('fl_r_borr') = 0.035;

[armt_map, func_map] = ffs_abz_get_funcgrid(param_map, support_map, bl_input_override); % 1 for override

default_params = {param_map support_map armt_map func_map};

%% Parse Parameters 1

% if varargin only has param_map and support_map,

params_len = length(varargin);

[default_params{1:params_len}] = varargin{:};

param_map = [param_map; default_params{1}];

support_map = [support_map; default_params{2}];

if params_len >= 1 && params_len <= 2

    % If override param_map, re-generate armt and func if they are not

    % provided

    bl_input_override = true;

    [armt_map, func_map] = ffs_abz_get_funcgrid(param_map, support_map, bl_input_override);

else

    % Override all

    armt_map = [armt_map; default_params{3}];

    func_map = [func_map; default_params{4}];

end

% append function name

st_func_name = 'ff_abz_vf';

support_map('st_profile_name_main') = [st_func_name support_map('st_profile_name_main')];

support_map('st_mat_name_main') = [st_func_name support_map('st_mat_name_main')];

support_map('st_img_name_main') = [st_func_name support_map('st_img_name_main')];

%% Parse Parameters 2

% armt_map

params_group = values(armt_map, {'ar_a', 'mt_z_trans', 'ar_z_r_borr_mesh_wage', 'ar_z_wage_mesh_r_borr'});

[ar_a, mt_z_trans, ar_z_r_borr_mesh_wage, ar_z_wage_mesh_r_borr] = params_group{:};

% func_map

params_group = values(func_map, {'f_util_log', 'f_util_crra', 'f_cons_checkcmin', 'f_coh', 'f_cons_coh'});

[f_util_log, f_util_crra, f_cons_checkcmin, f_coh, f_cons_coh] = params_group{:};

% param_map

params_group = values(param_map, {'it_a_n', 'it_z_n', 'fl_crra', 'fl_beta', 'fl_c_min',...

    'fl_nan_replace', 'bl_default', 'fl_default_aprime'});

[it_a_n, it_z_n, fl_crra, fl_beta, fl_c_min, ...

    fl_nan_replace, bl_default, fl_default_aprime] = params_group{:};

params_group = values(param_map, {'it_maxiter_val', 'fl_tol_val', 'fl_tol_pol', 'it_tol_pol_nochange'});

[it_maxiter_val, fl_tol_val, fl_tol_pol, it_tol_pol_nochange] = params_group{:};

% support_map

params_group = values(support_map, {'bl_profile', 'st_profile_path', ...

    'st_profile_prefix', 'st_profile_name_main', 'st_profile_suffix',...

    'bl_time', 'bl_display', 'it_display_every', 'bl_post'});

[bl_profile, st_profile_path, ...

    st_profile_prefix, st_profile_name_main, st_profile_suffix, ...

    bl_time, bl_display, it_display_every, bl_post] = params_group{:};

%% Initialize Output Matrixes

mt_val_cur = zeros(length(ar_a),it_z_n);

mt_val = mt_val_cur - 1;

mt_pol_a = zeros(length(ar_a),it_z_n);

mt_pol_a_cur = mt_pol_a - 1;

%% Initialize Convergence Conditions

bl_vfi_continue = true;

it_iter = 0;

ar_val_diff_norm = zeros([it_maxiter_val, 1]);

ar_pol_diff_norm = zeros([it_maxiter_val, 1]);

mt_pol_perc_change = zeros([it_maxiter_val, it_z_n]);

%% Iterate Value Function

% Loop solution with 4 nested loops

%

% # loop 1: over exogenous states

% # loop 2: over endogenous states

% # loop 3: over choices

% # loop 4: add future utility, integration--loop over future shocks

%

% Start Profile

if (bl_profile)

    close all;

    profile off;

    profile on;

end 

% Start Timer

if (bl_time) 

    tic; 

end 

% Utility at-Default/at-limiting-case-when-nodefault

if (fl_crra == 1) 

    fl_u_cmin = f_util_log(fl_c_min);

else 

    fl_u_cmin = f_util_crra(fl_c_min); 

end 

% Value Function Iteration

while bl_vfi_continue 

    it_iter = it_iter + 1; 

    %% Iterate over a and z states

    % Solve Problem if Default: coh < borr_bound, then: u(c_min) + EV(a'=0,z')

    % these are the values for defaulter

    % if do not borrow enough to pay debt: a'=0

    % if save more than what you have: a'=0

    % if borrowing, possible that all ar_val_cur values are

    % u(cmin), when that is the case, utility equal to

    % c_min, this means given current choice set, can only default,

    % get utility at c_min level, and a' go to 0. See

    % maximization over loop 3 choices for loop 1+2 states. see

    % <https://fanwangecon.github.io/CodeDynaAsset/docs/README_cminymin_borrsave.html

    % README_cminymin_borrsave> for additional discussions.

    %

    % when default is not allowed, there should be exactly one

    % element of the state space where we enter this condition.

    % That is at a_min and z_min. At this point, the natural

    % borrowing constraint when fully used up leads to c = 0.

    % When default is not allowed, this is the limiting case.

    % We solve the limiting case as if default is possible. see

    % the figure here:

    % <https://fanwangecon.github.io/CodeDynaAsset/m_az/test/ffs_abz_get_funcgrid/test_borr/html/ffs_abz_get_funcgrid_nodefault.html

    % ffs_abz_get_funcgrid_nodefault>. For the figure under

    % section *Generate Borrowing A Grid with Default*, there are

    % no points to the lower right of the red horizontal and

    % verticle lines, because no default is allowed. But the

    % intersection of the two red lines is this limiting case

    % where c = 0.

    %

    % when default is allowed. See again

    % <https://fanwangecon.github.io/CodeDynaAsset/m_az/test/ffs_abz_get_funcgrid/test_borr/html/ffs_abz_get_funcgrid_nodefault.html

    % ffs_abz_get_funcgrid_nodefault>. Again under section

    % *Generate Borrowing A Grid with Default*, see that there

    % is an area to the right bottom of the two blue horizontal

    % and vertical lines. For all points in that area, the

    % household has to default, they can not borrow even at max

    % to get positive consumption. At other points higher than

    % the blue horizontal line, it is also possible for

    % defaulting to be the optimal choice.

    % loop 1: over exogenous states

    for it_z_i = 1:it_z_n 

        % Current Shock

        fl_z_r_borr = ar_z_r_borr_mesh_wage(it_z_i); 

        fl_z_wage = ar_z_wage_mesh_r_borr(it_z_i); 

        % loop 2: over endogenous states

        for it_a_j = 1:length(ar_a) 

            fl_a = ar_a(it_a_j); 

            ar_val_cur = zeros(size(ar_a)); 

            % calculate cash on hand

            fl_coh = f_coh(fl_z_r_borr, fl_z_wage, fl_a); 

            % loop 3: over choices

            for it_ap_k = 1:length(ar_a) 

                % get next period asset choice

                fl_ap = ar_a(it_ap_k); 

                % calculate consumption

                fl_c = f_cons_coh(fl_coh, fl_ap); 

                % assign u(c)

                if (fl_c <= fl_c_min) 

                    if (bl_default) 

                        % defaults

                        % current utility: only today u(cmin)

                        ar_val_cur(it_ap_k) = fl_u_cmin; 

                        % transition out next period, debt wiped out

                        for it_az_q = 1:it_z_n 

                            ar_val_cur(it_ap_k) = ar_val_cur(it_ap_k) + ... 

                                fl_beta*mt_z_trans(it_z_i, it_az_q)*mt_val_cur((ar_a == fl_default_aprime), it_az_q); 

                        end 

                    else

                        % if default is not allowed: v = fl_nan_replace

                        ar_val_cur(it_ap_k) = fl_nan_replace;

                    end 

                else 

                    % Solve Optimization Problem: max_{a'} u(c(a,a',z)) + beta*EV(a',z')

                    % borrowed enough to pay debt (and borrowing limit not exceeded)

                    % saved only the coh available.

                    % current utility

                    if (fl_crra == 1) 

                        ar_val_cur(it_ap_k) = f_util_log(fl_c);

                    else 

                        ar_val_cur(it_ap_k) = f_util_crra(fl_c); 

                    end 

                    % loop 4: add future utility, integration--loop over future shocks

                    for it_az_q = 1:it_z_n 

                        ar_val_cur(it_ap_k) = ar_val_cur(it_ap_k) + ... 

                            fl_beta*mt_z_trans(it_z_i, it_az_q)*mt_val_cur(it_ap_k, it_az_q); 

                    end 

                end 

            end 

            % optimal choice value

            [fl_opti_val_z, fl_opti_idx_z] = max(ar_val_cur); 

            fl_opti_aprime_z = ar_a(fl_opti_idx_z); 

            fl_opti_c_z = f_cons_coh(fl_coh, fl_opti_aprime_z); 

            % Handle Default is optimal or not

            if (fl_opti_c_z <= fl_c_min) 

                if (bl_default) 

                    % if defaulting is optimal choice, at these states, not required

                    % to default, non-default possible, but default could be optimal

                    fl_opti_aprime_z = fl_default_aprime; 

                else

                    % if default is not allowed, then next period same state as now

                    % this is absorbing state, this is the limiting case, single

                    % state space point, lowest a and lowest shock has this.

                    fl_opti_aprime_z = fl_a;

                end 

            end 

            %% Store Optimal Choices and Value Given(a,z)

            mt_val(it_a_j,it_z_i) = fl_opti_val_z; 

            mt_pol_a(it_a_j,it_z_i) = fl_opti_aprime_z; 

        end 

    end 

    %% Check Tolerance and Continuation

    % Difference across iterations

    ar_val_diff_norm(it_iter) = norm(mt_val - mt_val_cur); 

    ar_pol_diff_norm(it_iter) = norm(mt_pol_a - mt_pol_a_cur); 

    mt_pol_perc_change(it_iter, :) = sum((mt_pol_a ~= mt_pol_a_cur))/(it_a_n); 

    % Update

    mt_val_cur = mt_val; 

    mt_pol_a_cur = mt_pol_a; 

    % Print Iteration Results

    if (bl_display && (rem(it_iter, it_display_every)==0)) 

        fprintf('VAL it_iter:%d, fl_diff:%d, fl_diff_pol:%d\n', ...

            it_iter, ar_val_diff_norm(it_iter), ar_pol_diff_norm(it_iter));

        tb_valpol_iter = array2table([mean(mt_val_cur,1); mean(mt_pol_a_cur,1); ...

            mt_val_cur(it_a_n,:); mt_pol_a_cur(it_a_n,:)]);

        tb_valpol_iter.Properties.VariableNames = strcat('z', string((1:size(mt_val_cur,2))));

        tb_valpol_iter.Properties.RowNames = {'mval', 'map', 'Hval', 'Hap'};

        disp('mval = mean(mt_val_cur,1), average value over a')

        disp('map  = mean(mt_pol_a_cur,1), average choice over a')

        disp('Hval = mt_val_cur(it_a_n,:), highest a state val')

        disp('Hap = mt_pol_a_cur(it_a_n,:), highest a state choice')

        disp(tb_valpol_iter);

    end

    % Continuation Conditions:

    % 1. if value function convergence criteria reached

    % 2. if policy function variation over iterations is less than

    % threshold

    if (it_iter == (it_maxiter_val + 1)) 

        bl_vfi_continue = false; 

    elseif ((it_iter == it_maxiter_val) || ... 

            (ar_val_diff_norm(it_iter) < fl_tol_val) || ... 

            (sum(ar_pol_diff_norm(max(1, it_iter-it_tol_pol_nochange):it_iter)) < fl_tol_pol)) 

        % Fix to max, run again to save results if needed

        it_iter_last = it_iter; 

        it_iter = it_maxiter_val; 

    end 

end 

% End Timer

if (bl_time) 

    toc; 

end 

% End Profile

if (bl_profile) 

    profile off 

    profile viewer

    st_file_name = [st_profile_prefix st_profile_name_main st_profile_suffix];

    profsave(profile('info'), strcat(st_profile_path, st_file_name));

end

%% Process Optimal Choices

result_map = containers.Map('KeyType','char', 'ValueType','any');

result_map('mt_val') = mt_val;

result_map('cl_mt_coh') = {f_coh(ar_z_r_borr_mesh_wage, ar_z_wage_mesh_r_borr, ar_a'), zeros(1)};

result_map('cl_mt_pol_a') = {mt_pol_a, zeros(1)};

result_map('cl_mt_pol_c') = {f_cons_checkcmin(ar_z_r_borr_mesh_wage, ar_z_wage_mesh_r_borr, ar_a', mt_pol_a), zeros(1)};

result_map('ar_st_pol_names') = ["cl_mt_pol_a", "cl_mt_coh", "cl_mt_pol_c"];

if (bl_post)

    bl_input_override = true;

    result_map('ar_val_diff_norm') = ar_val_diff_norm(1:it_iter_last);

    result_map('ar_pol_diff_norm') = ar_pol_diff_norm(1:it_iter_last);

    result_map('mt_pol_perc_change') = mt_pol_perc_change(1:it_iter_last, :);

    result_map = ff_az_vf_post(param_map, support_map, armt_map, func_map, result_map, bl_input_override);

end

end